Rack and pinion: a design guide to turning rotation into linear motion

How rack and pinion works

A rack is a gear with infinite pitch radius, so its flanks are straight. As the pinion turns it drives the rack linearly — used on long CNC axes, sliding doors, steering and grippers. Compared with a lead screw it offers virtually unlimited travel and high speed, but backlash and stiffness need attention.

Pairing rules and mounting distance

• Rack and pinion must share the same module.
• And the same pressure angle (usually 20°).
• The pinion's pitch circle must touch the rack's pitch line.

Pinion centre to rack base = (H − m) + m · z / 2

H is the rack's overall height and H − m its pitch-line height. m1, 10 mm rack, 20-tooth pinion: 9 + 10 = 19 mm. Add 0.05–0.1 mm for clearance.

Travel per revolution and resolution

Travel per revolution = π · m · z

Resolution = (360 / step angle × microsteps) ÷ travel per revolution. For finer resolution, use fewer teeth, a smaller module, or a reduction stage.

Tips for 3D-printed racks

• Longer than your bed? Print segments with whole tooth counts so the pitch stays continuous; join with dovetails or dowels.
• Print teeth-up, lying flat, for the best flank surface and strength.
• Use about 0.1 mm backlash on FDM; long racks warp — thicken the base or use PETG / nylon.
• For heavy loads or low backlash, use a helical rack or SLS nylon.